Multiple choice

From a pack of cards, two are drawn, the first being replaced before the second is drawn. Find the probability that the first is a club and the second is a red card.

  1. $\dfrac{1}{52}$
  2. $\dfrac{1}{26}$
  3. $\dfrac{1}{8}$
  4. $\dfrac{4}{13}$
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C Correct answer
Explanation

Probability of first card being a club = 13/52 = 1/4. Probability of second card being a red card (hearts or diamonds) = 26/52 = 1/2. Since the first is replaced, the events are independent. Total probability = (1/4) * (1/2) = 1/8.

AI explanation

Since the first card is replaced, the two draws are independent events. The probability of drawing a club is 13/52, which is 1/4, and the probability of drawing a red card is 26/52, which is 1/2. By the multiplication rule for independent events, the combined probability is (1/4) times (1/2), which equals 1/8.

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